8v^2-v-19=0

Solution for 8v^2-v-19=0 equation:

8v^2-v-19=0

We add all the numbers together, and all the variables

8v^2-1v-19=0

a = 8; b = -1; c = -19;
Δ = b2-4ac
Δ = -12-4·8·(-19)
Δ = 609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{609}}{2*8}=\frac{1-\sqrt{609}}{16}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{609}}{2*8}=\frac{1+\sqrt{609}}{16}
$